NCERT Book Class 6 Maths Mensuration

Mensuration

10.1 Introduction

When we talk about some plane figures as shown below we think of their regions and their boundaries. We need some measures to compare them. We look into these now.

10.2 Perimeter

Look at the following figures (Fig. 10.1). You can make them with a wire or a string. If you start from the point S in each case and move along the line segments then you again reach the point S. You have made a complete round of the shape in each case (a), (b) & (c). The distance covered is equal to the length of wire used to draw the figure. This distance is known as the perimeter of the closed figure. It is the length of the wire needed to form the figures.

The idea of perimeter is widely used in our daily life.

• A farmer who wants to fence his field.
• An engineer who plans to build a compound wall on all sides of a house.
• A person preparing a track to conduct sports.

All these people use the idea of ‘perimeter’.

Give five examples of situations where you need to know the perimeter. Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once.

10.2.1 Perimeter of a rectangle

Let us consider a rectangle ABCD (Fig 10.2) whose length and breadth are 15 cm and 9 cm respectively. What will be its perimeter?

Perimeter of the rectangle = Sum of the lengths of its four sides.

                                      = AB + BC + CD + DA

                                      = AB + BC + AB + BC

                                      = 2 × AB + 2 × BC

                                      = 2 × (AB + BC)

                                      = 2 × (15cm + 9cm)

                                      = 2 × (24cm)

                                      = 48 cm

Hence, from the said example, we notice that 

Perimeter of a rectangle       = length + breadth + length + breadth

i.e. Perimeter of a rectangle = 2 × (length + breadth)

Let us now see practical applications of this idea :

Example 1 : Shabana wants to put a lace border all around a rectangular table cover (Fig 10.3), 3 m long and 2 m wide. Find the length of the lace required by Shabana.

Solution : Length of the rectangular table cover    = 3 m

                Breadth of the rectangular table cover   = 2 m

Shabana wants to put a lace border all around the table cover. Therefore, the length of the lace required will be equal to the perimeter of the rectangular table cover.

10.2.2 Perimeter of regular shapes

Consider this example.

Biswamitra wants to put coloured tape all around a square picture (Fig 10.5) of side 1m as shown. What will be the length of the coloured tape he requires?

Since Biswamitra wants to put the coloured tape all around the square picture, he needs to find the perimeter of the picture frame. Thus, the length of the tape required

          = Perimeter of square = 1m + 1 m + 1 m + 1 m = 4 m

Now, we know that all the four sides of a square are equal, therefore, in place of adding it four times, we can multiply the length of one side by 4.

Thus, the length of the tape required = 4 × 1 m = 4 m From this example, we see that

Perimeter of a square = 4 × length of a side

Draw more such squares and find the perimeters. Now, look at equilateral triangle (Fig 10.6) with each side equal to 4 cm. Can we find its perimeter?

Perimeter of this equilateral triangle = 4 + 4 + 4 cm = 3 × 4 cm = 12 cm

Please refer to attached file for NCERT Class 6 Maths Mensuration